Answer:
L - h = 12.3672 in
Explanation:
Given
P = 41.0 lb/in² = 41 P.S.I
L = 16.8 in
A = 3.00 in²
h = ?
In order that air flows into the tire, the pressure in the pump must be more than the tire pressure, 41.0 PSI.
We assume that air follows ideal gas equation, the temperature of the compressed air remains constant as the piston moves down. Taking one atmospheric pressure to be 14.6959 P.S.I , we can use the ideal gas equation
P*V = n*R*T
As number of moles of air do not change during its compression in the pump, n*R*T of the gas equation is constant. Therefore we have
P₁*V₁ = P₂*V₂ ⇒ V₂ = P₁*V₁ / P₂
where
1 and 2 are initial and final states respectively,
V₁ = A*L = (3.00 in²)*(16.8 in) ⇒ V₁ = 50.4 in³
P₁ = 14.6959 P.S.I
P₂ = P₁ + P = (14.6959 lb/in²) + (41.0 lb/in²) = 55.6959 lb/in²
Inserting various values we get
V₂ = (14.6959 P.S.I)*(50.4 in³) / (55.6959 lb/in²)
⇒ V₂ = 13.2985 in³
Length of pump, measured from bottom, this volume corresponds to is
h = V₂ / A = (13.2985 in³) / (3.00 in²)
⇒ h = 4.4328 in
Piston must be pushed down by more than
L - h = 16.8 in - 4.4328 in = 12.3672 in
